When I leveled my s-priest (late cata/early MoP), my only complaint was that you go OOM ridiculously fast so in that aspect disc can be better.
I say level as disc for early levels (till about 70 or so) then go shadow for the power increase.

---------- Post added 2013-05-21 at 12:21 AM ----------

Originally Posted by Rebden

Ahh, i see, so disc is also good for healing am i correct?

Disc is actually just a heal spec, not dps in the slightest.
HOWEVER
You can deal damage with smite/holy fire and heal for 50% of the damage caused. This is pretty powerful early on when soloing/ healing 5-mans

if you're planning on dungeon running then i still recommend holy for new priests. disc is smite smite smite smite smite shield smite etc etc. holy you get to learn what your other buttons do. you will struggle with questing though, if you're planning on doing lots of questing or pvp, then go disc

I have been playing a priest for 4 years now. I recently rolled a new one on a medium pop server to play with some people via a podcast guild.

I'm level 26 right now and what I did was went disc to this point. you can level with popping shadow word: pain, then smiting and using penance offensively.

At 27 you get vampiric touch as shadow so I recommend going shadow then. you'll use vampiric touch, shadow word: pain, and mind blast with filling in mind flay while your dots tick. when you get 3 shadow orbs (you get these upon using mind blast) then you'll use devouring plague to deal more damage. try and save devouring plague for a higher health mob though when questing as it gets wasted on lower health mobs.

So my advice... disc to 27 then shadow from there on. If you want to do dungeons decide if you want to heal or dps. if heal then holy or disc. disc would be better if you want to quest while waiting in que (healer que at lower levels can be a bit long too since so many people are trying it). Go shadow if you just want to purely quest with mixing in a dungeon or two while doing it.

Oh one last note. get the glyph that lets you use renew while in shadowform. this will help while leveling. you can use renew without coming out of shadow so it'll tick while you damage

I rolled a priest to 90 as shadow. It was fun, and I really liked it a lot. I have a hard time just swapping specs out, and have been wanting to try to heal so I decided to roll a Disc to level with some friends and I love it. I can kill stuff and heal, it rules. I haven't healed in an instance yet (just dinged 15 last night) but I expect it will be fun. I don't think you can go wrong though, choose what you think sounds the most fun

Edit: Mind sear for AOE. In instances use power word shield on the tank then mind sear away.

Shadow is awesome to play, I found it generally interesting. If you want to heal I'd recommend starting with Disc to get a feel for things, then moving to holy (which requires mana management) at later levels

Originally Posted by notorious98

I hear in order to get the browser attunement, you first had to run heroic Internet.

If you want to run Dungeons, don't go Shadow before lvl 76, when you get Mind Sear, your first AOE spel. Becouse low level instances are AOE fests and you will feal completely useles as a Shadow. Before you even try to DoT all mobs up, they would probably all be dead Disc is about the same dmg as Shadow ( from lvl 10 to 80) + healing + more survivability. Holy is also great dmg when you get Chakras.

If you want to run Dungeons, don't go Shadow before lvl 76, when you get Mind Sear, your first AOE spel. Becouse low level instances are AOE fests and you will fill completely useles as a Shadow. Before you even try to DoT all mobs up, they would probably all be dead Disc is about the same dmg as Shadow ( from lvl 10 to 80) + healing + more survivability. Holy is also great dmg when you get Chakras.

Pretty much this, dungeons lower level are an aoe fest and shadow suffers from having none till level 76. All that dotting thing is frustrating when mobs die before your SWP got to tick 3 times, especially with a tank that knows how to play/has heirlooms.

And one correction to somebody that posted above: atonement (the disc heal from dmg tool) does 100% of the dmg as healing, not 50%. It's only limited to 50% if it heals the priest that casted it. Otherwise, you can largely be a dps in dungeons and heal passively more or less till 80 and still do a fair bit of that even after. The downside is that its a really simple rotation, you might get bored out of your mind to spam 3 spells. Nobody prevents you from using the same spells as holy, its just not really needed as long as you dps most of the times.